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Sergei Zuyev 
This page contains add-ons to some of my papers. Something special that has not found its place on the journals' pages. 


Course given at 25th Finnish Summer School on Probability Theory, Nagu/Nauvo, The Archipelago of Finland, 2-6 of June, 2003

Measures Everywhere

  • Lecture 1. Variation analysis on measures
  • Lecture 2. Design of experiments
  • Lecture 3 Variation analysis for Poisson processes
  • Lecture 4 High intensity optimisation
  • Lecture 5 Numerical optimisation
  • Lecture 6 Applications
    • . 
    To the paper: A. Lindo, S. Zuyev and S. Sagitov

    Nonparametric estimation of infinitely divisible distributions based on variational analysis on measures

    In this paper we develop algorithms of steepest descent type to estimate the compounding measure of a sample distributed as compound Poisson. They are realised in our R-library mesop (the source code). It realises the steepest descent method to find extremum for a strongly differentiable functional of a measure in the class of positive measures without any additional constraints. To see example of its use, see the example provided in man(GoSteep).
    To the paper: M. Zolghadr and S. Zuyev

    Optimal design of dilution experiments under volume constraints

    The paper aims at finding optimal designs of dilution experiments under the total volume constraint typical for stem cells research. Here is the R-code providing the designs described in the paper. It also uses medea R-library available for download at the bottom of this page. 
    To the paper: X. Li, D. K. Hunter and S. Zuyev

    Coverage Properties of the Target Area in Wireless Sensor Networks

    The paper studies tri-covered areas with respect to a two-dimensional Poisson process representing wireless sensors. Two scripts in freely available Statistical Programming language R are provided. The code triang-simul.R estimates the density of tri-covered area by Monte-Carlo simulations, the code triang-estim.R provides a lower analytical bound, see the paper for details. Both scripts are extensively commented and contain examples of the usage. 
    To the paper: K. Tchoumatchenko and S. Zuyev

    Aggregate and fractal tessellations

    These tessellations are defined as follows. Let C0(X0i) be tessellation's cells of level 0 with the nuclei X0i , i=1...N0. To construct an aggregate tessellation of level 1 consider a 1-st level tessellation {C1(X1j)} with nuclei {X1j}, j=1...N1. Now the aggregate cells of level 1 are the sets C10(X0i) associated with the 0-level nuclei X0i that are the union of those C1(X1j) whose nuclei X1j lie inside C0(X0i). Given a 2nd-level tessellation {C2(X2k)}, the second level aggregate cells C20(X0i) are the union of those C2(X2k) having X2k belonging to C10(X0i), etc., etc... This construction allows to obtain very wierd tessellations with the cells that are generally not convex, not connected and do not necessarily contain the nucleus. You can download my program called pvat that draws Poisson-Voronoi aggregate tessellations. Here is a screen-shot of how they look in pvat.
    To the paper: I. Molchanov and S. Zuyev

    Steepest descent algorithms in space of measures

    In this paper propose a "true" steepest descent method for optimisation of functionals defined on non-negative measures. The corresponding algorithms are encoded in Splus and R languages and available as source R-libraries mefista (for finding an optimal measures with a fixed total mass) and and medea (for optimisation under many constraints). Windows binaries (compiled under R version 3) are: mefista.zip and medea.zip.
    To the paper: I. Molchanov and S. Zuyev

    Optimisation in space of measures and optimal design

    In this paper we propose a unified approach to finding an optimal design measure. In a common case when an analytical solution is impossible, the steepest descent algorithms described in the previous paper allow for a numerical solution. This could be done with the help of our R-libraries mefista (for finding an optimal measures with a fixed total mass) and and medea (for optimisation under many constraints). Windows binaries (compiled under R version 3) are: mefista.zip and medea.zip. Here is a screen-shot from an R-window.